Coefficient of a32 in the binomial expansion of a 4-1- a 315 is-A- 0B- 15 C 4C- 15 C 4D- None

The correct option is B 15C4 T_r+1 = ^15 C _r(a^4)^15 r( 1/a^3)^r Equating power of a to 32 60 7r = 32 then r = 4 ...

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Standard XII

Mathematics

Binomial Expression

Coefficient o...

Question

Coefficient of a32 in the binomial expansion of ${(a^{4} - \frac{1}{a^{3}})}^{15}$ is:

¹⁵C₄

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-¹⁵C₄

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None

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Solution

The correct option is A
¹⁵C₄

$T_{r + 1}$ = $^{15} C_{r}$ $(a^{4})^{15 - r} {(- \frac{1}{a^{3}})}^{r}$

Equating power of a to 32

60-7r = 32 then r = 4

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Similar questions

Q. Coefficient of

a^{32}

in the expansion of

(a^{4} - \frac{1}{a^{3}})^{15}

Prove that the coefficient of $x^{n}$ in the binomial expansion of $(1 + x)^{2 n}$ is twice the coefficient of $x^{n}$ in the binomial expansion of $(1 + x)^{2 n - 1}$ .

The value of $1. C_{1} + 3. C_{3} + 5. C_{5} + 7. C_{7} + . . . . w h e r e C_{0}, C_{1}, C_{2} . . . . . C_{n}$ are binomial coefficients in the expansion of $(1 + x)^{n}$ is: